The adjustment of crustal motion parameters in satellite geodetic networks

Global satellite networks of the highest accuracy are needed for all geodynamic investigations. The investigation of possible changes in the inner geometry of the station network is necessary because such changes would influence the determination of polar coordinates, length of day and other parameters.The different possibilities for such investigations (epoch-related coordinate sets, adjustment of station motions, determination of global kinematic plate parameters) are discussed in detail. The estimable parameters describing crustal motions are pointed out.Laser-ranging data from the LAGEOS satellite during the MERIT Campaign are used for practical computations. These computations demonstrate an accuracy for distance determinations below the decimeter level. The time span of the data (14 months) is not sufficient for the computation of significant station motions, but it is valuable for evaluation of the model's accuracy.     

Gravity potential at the Major Vertical Datum as primary geodetic constant

Summary On the basis of the fundamental relations of the Molodensky's Earth's figure theory (1945), admitting the inequality of the gravity potentials at the Major Vertical Datum W₀ and on the surface of the reference level ellipsoid U₀, and taken into account that potential W₀ enters into equations directly, it is recomended, W₀ should be adopted as a primary geodetic constant. Parameters of the best fitting ellipsoid are not needed for the solution of geodetic problems and for the investigation of the Earth's gravity field. The reason for requiring the reference and actual fields be close is only that the boundary-value problem can be solved in the linear approximation. Dedicated to the Memory of M.S. Molodensky Contribution to the I.A.G. Special Commission SC3 Fundamental Constants (SCFC).     

大地形变流动观测数据库

为有效管理大地形变流动观测数据,基于关系型数据库设计大地形变流动观测数据库,完成区域精密水准、流动GNSS、流动重力、跨断层场地观测数据的结构化存储,实现了观测过程数据（包括观测数据和管理数据）的规范化管理,从而有效控制了大地形变流动观测数据质量,提高了数据质量管理效率。     

On the geodetic control systems

Summary In this article the local, nation-wide and world-wide geodetic control systems will be treated as well as the advantage and limitation of the geodetic adjustments of large triangulation nets, and the additional observations needed before the second adjustment of the European triangulation. The fundamental significance of the gravimetric method for establishing the world-wide geodetic system, for the control of small scale maps beginning from 1100.000 for determining of the super control points for the long-range triangulations and particulary for checking the earth's dimensions will be emphasized.

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Zusammenfassung In diesem Aufsatze werden die lokalen, nationalen und weltweiten geodätischen Systeme behandelt, vor zu grossem Vertrauen in die Ausgleichsrechnungen gewarnt, einige Vorbedingungen für gute Ausgleichung der Europäischen Triangulation erwähnt, die Bedeutung der gravimetrischen Methode für das weltweite geodätische System, für Kontrolle der Karten von kleinem Masstabe (nicht grösser als 1100.000), für Berechnung der Erddimensionen und für Gründung der Superkontrollpunkte für die grossen Triangulationen betont.

     

A new approach to geodetic networks

Studia Geophysica et Geodaetica - The linearized model of a geodetic network, expressed by the relationv=A h−I, does not generally satisfy the following conditions: Therefore, intermediary...     

Fundamental geodetic parameters of the earth's figure and the structure of the earth's gravity field derived from satellite data

Summary Using the geocentric constant GM=398 601.3 × 10 ⁹ m ³s ^–2 , the known value of the angular velocity of the Earth's rotation , Stokes' constants J _n ^(k) and S _n ^(k) upto n=21 (zonal), n=16 (tesseral and sectorial) [2], the geocentric co-ordinates and heights above sea-level of SAO satellite stations [2], the following will be derived: the potential on the geoid W_o, the scale factor for lengths R_o=GM/W_o, the radius-vector of the surface W=W_o, the parameters of the best-fitting Earth tri-axial ellipsoid, and the components of the deflections of the vertical with respect to the geocentric rotational IAG ellipsoid (Lucerne 1967), as well as to the best-fitting geocentric tri-axial ellipsoid. Some of the differences in the structure of the gravity field over the Northern and Southern Hemispheres will be given, and the mean values of gravity over the equatorial zone, determined from the dynamics of satellite orbits, on the one hand, and from terrestrial gravity data, on the other, will be compared.Presented at the Fifteenth IUGG General Assembly, Moscow, July 30 — August 14, 1971.     

The need for a better defined Egyptian geodetic datum for geodynamic studies

One of the main objectives of geodesy is to establish a framework of well distributed points (geodetic control points). The coordinates of these points should be known with sufficient accuracy in order to detect any crustal movement and to be also used in any application of geodynamics. These in turn need a better defined geodetic datum.Unfortunately, in Egypt such datum has not yet been adopted due to the lack in geodetic observations. The adopted ellipsoid is not the best or even a good fit to the geoid in Egypt. Therefore, the geodetic observations have not been completely and rigorously reduced to the reference ellipsoid. The network suffers from a fairly large distortion in scale and orientation. Quite a part of that distortion is due to the lack in reducing such observations. The objective of this paper is to review both the available geodetic data and to propose an approach to achieve a well defined geometric datum. Such approach should use all types of geodetic observations (astro-gravity-Doppler) in a combined study using a least squares collocation technique.     

Seafloor geodetic network establishment and key technologies

Seafloor geodetic network construction involves the development of geodetic station shelter, network configuration design, location selection and layout, surveying strategy, observation model establishment and optimization, data processing strategy and so on. This paper tries to present main technological problems involved in the seafloor geodetic network construction, and seek the technically feasible solutions. Basic conceptions of developing seafloor geodetic station shelters for shallow sea and deep-sea are described respectively. The overall criteria of seafloor geodetic network construction for submarine navigation and those of network design for crustal motion monitoring are both proposed. In order to enhance application performances of the seafloor geodetic network, the seafloor network configuration should prefer a symmetrical network structure. The sea surface tracking line measurements for determining the seafloor geodetic station position should also adopt an approximately symmetrical configuration, and we recommend circle tracking line observations combined with cross-shaped line(or double cross-shape line) observations for the seafloor positioning mode. As to the offset correction between the Global Navigation Satellite System antenna phase center and the acoustic transducer, it is recommended to combine the calibration through external measurements and model parameter estimation. Besides, it is suggested to correct the sound speed error with a combination of observation value correction and parameterized model correction, and to mainly use the model correction to reduce the influence of acoustic ray error on the seafloor positioning. Following the proposed basic designs, experiments are performed in shallow sea area and deep-sea area respectively. Based on the developed seafloor geodetic shelter and sufficient verification in the shallow sea experiment, a long-term seafloor geodetic station in the deep-sea area of 3000 m depth was established for the first time, and the preliminary positioning result shows that the internal precision of this station is better than 5 cm.     

Closed-form transformation between geodetic and ellipsoidal coordinates

We present formulas for direct closed-form transformation between geodetic coordinates (φ, λ, h) and ellipsoidal coordinates (β, λ, u) for any oblate ellipsoid of revolution. These will be useful for those dealing with ellipsoidal representations of the Earth’s gravity field or other oblate ellipsoidal figures. The numerical stability of the transformations for near-polar and near-equatorial regions is also considered.     

Results of new geodetic investigations in SW-Germany

A general overview of temporal height changes in SW-Germany is given. Based on first-order levelling data, the height changes are estimated using kinematic models. The results are presented in maps by isolines. For a first geodetic interpretation, examples of trend-analysis and calculations of horizontal gradients are used. Areas with trends of uplift and subsidence are recognizable. Finally, the geodetic results are compared with other geoscientific conceptions.     

The 2011 Tohoku-Oki earthquake's influence on the Asian plates and Korean geodetic network

本研究分析了2011年3月11日发生的Mw9.0日本东北地区太平洋近海地震对亚洲地区和韩国国内GPS卫星常年跟踪站的位移影响.为此,利用了日本东北地区太平洋近海地震发生前后两周(2011年3月4日到3月18日)的GPS站点数据,包括震中附近地区(韩国,中国,中国台湾地区,日本和俄罗斯)55个GPS卫星常年跟踪站和284个IGS全球跟踪站,并采用GAMIT/GL,OBK软件进行处理和平差,估算出所有GPS站点的同震形变.结果显示,日本东北地区太平洋近海地震引起的同震形变影响在亚洲地区比较明显,包括日本和附近国家,距离震中2702 km的中国武汉(WUHN)站也观测到同震形变.为精确分析日本东北地区太平洋近海地震对韩国国家大地控制网的影响.通过GAMIT/GLLOBK软件计算出韩国GPS卫星常年跟踪站之间的基线长度变形,并分析出弹性变形量.结果表明:大部分GPS站点均向震中方向膨胀,且向震中的垂直方向收缩,由日本东北地区太平洋近海地震导致的最大剪应变达到韩国国家大地控制网年均变形率的约7倍,对韩国的地壳产生14.5～57.7 mm的水平位移,并导致韩国国家大地控制网产生弹性变形,因此,在不及时更新维护韩国国家大地控制网的情况下,GPS测量成果将会发生最大20 mm的位置误差.     

Geocenter motion and its geodetic and geophysical implications

The horizontal transport of water in Earth's surface layer, including sea level change, deglaciation, and surface runoff, is a manifestation of many geophysical processes. These processes entail ocean and atmosphere circulation and tidal attraction, global climate change, and the hydrological cycle, all having a broad range of spatiotemporal scales. The largest atmospheric mass variations occur mostly at synoptic wavelengths and at seasonal time scales. The longest wavelength component of surface mass transport, the spherical harmonic degree-1, involves the exchange of mass between the northern and southern hemispheres. These degree-1 mass loads deform the solid Earth, including its surface, and induce geocenter motion between the center-of-mass of the total Earth system (CM) and the center-of-figure (CF) of the solid Earth surface. Because geocenter motion also depends on the mechanical properties of the solid Earth, monitoring geocenter motion thus provides an additional opportunity to probe deep into Earth's interior. Most modern geodetic measurement systems rely on tracking data between ground stations and satellites that orbit around CM. Consequently, geocenter motion is intimately related to the realization of the International Terrestrial Reference Frame (ITRF) origin, and, in various ways, affects many of our measurement objectives for global change monitoring. In the last 15 years, there have been vast improvements in geophysical fluid modeling and in the global coverage, densification, and accuracy of geodetic observations. As a result of these developments, tremendous progress has been made in the study of geocenter motion over the same period. This paper reviews both the theoretical and measurement aspects of geocenter motion and its implications.     

The western desert — an example for geodetic problems in arid areas

In this paper some methodical aspects concerning the construction of an accurate geodetic network in arid areas and the connection of the new points to an existing network are discussed. In this context special attention is rapid on the determination of the station heights above the geoid. For the Western Desert in Egypt, which can be regarded as an example of an arid, geodetically underdeveloped region, an observational program is outlined that combines Doppler-measurements with an astrogravimetric-levelling.     

Statistical analysis of values measured in condensating geodetic nets

Summary Procedure for verifying the agreement between parameters common to the basic and connecting trigonometric net. Procedure of determining the accuracy of the connecting net. This determination concerns not only the relativized accuracy of the points of the connecting network, but also the mutual accuracy of the points of the basic net relative to the points of the connecting net and the global accuracy of the resultant net. The procedure takes into account the accuracy of the points of the basic net which remain unchanged in computing the coordinates of new points.

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The quasi-isotropic relative structure of a geodetic net and the procedure used to establish it

Summary The method of computing the quasi-isotropic relative structure (QIRS) of a geodetic net which maximizes the relative accuracy between a priori determined points of the net, the configuration of the net being taken into account, is described. The iteration procedure is used to establish this structure.

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Error propagation in absolute geodetic networks a continuous approach

Summary Studies of error propagation in geodetic networks of an absolute type have already been carried through by several authors using various mathematical techniques. The geodetic elasticity theory relies on a continuation of the actual, discrete network. The traditional observation and normal equation matrices are substituted by partial differential equations with corresponding boundary conditions. The continuous approach only reflects the global error behaviour opposed to the discrete case, and produces only asymptotic results. An advantage of the method is that we may directly profit from existing mathematical knowledge. The fundamental solution of the partial differential equations acts as a formal covariance function and yields the best linear unbiased estimates for estimable functions of the adjustment parameters. Levelling networks and networks with distance and azimuth measurements are studied in this framework.Invited paper presented at the International Symposium on Optimisation of Design and Computation of Control Networks, Sopron, July 4–8, 1977.     

Some geophysical and geodetic contributions of satellite-determined gravity results

Satellite orbital data yield reliable values of low degree and order coefficients in the spherical harmonic expansion of the Earth's gravity field. The second degree coefficient yields the shape of the Earth — probably the most important single parameter in geodesy. It is crucial in the numerical evaluation of different forms of the theoretical gravity formula. The new information requires the standardization of gravity anomalies obtained from satellite gravity and terrestrial gravity data in the context of three most commonly used reference figures, e.g.,International Reference Ellipsoid, Reference Ellipsoid 1967, andEquilibrium Reference Ellipsoid. This standardization is important in the comparison and combination of satellite gravity and gravimetric data as well as the integration of surface gravity data, collected with different objectives, in a single reference system.Examination of the nature of satellite gravity anomalies aids in the geophysical and geodetic interpretation of these anomalies in terms of the tectonic features of the Earth and the structure of the Earth's crust and mantle. Satellite results also make it possible to compute the Potsdam correction and Earth's equatorial radius from the satellite-determined geopotential. They enable the decomposition of the total observed gravity anomaly into components of geophysical interest. They also make it possible to study the temporal variations of the geogravity field. In addition, satellite results make significant contributions in the prediction of gravity in unsurveyed areas, as well as in providing a check on marine gravity profiles.On leave from University of Hawaii, Honolulu.     

A Brovar-type solution of the fixed geodetic boundary-value problem

For more than 150 years gravity anomalies have been used for the determination of geoidal heights, height anomalies and the external gravity field. Due to the fact that precise ellipsoidal heights could not be observed directly, traditionally a free geodetic boundary-value problem (GBVP) had to be formulated which after linearisation is related to gravity anomalies. Since nowadays the three-dimensional positions of gravity points can be determined by global navigation satellite systems very precisely, the modern formulation of the GBVP can be based on gravity disturbances which are related to a fixed GBVP using the known topographical surface of the Earth as boundary surface. The paper discusses various approaches into the solution of the fixed GBVP which after linearization corresponds to an oblique-derivative boundary-value problem for the Laplace equation. Among the analytical solution approaches a Brovar-type solution is worked out in detail, showing many similarities with respect to the classical solution of the scalar free GBVP.     

利用大地测量数据反演地震位错Love数和格林函数的理论与方法

本文提出一种利用大地测量观测技术反演地震位错Love数及格林函数的理论和方法.首先根据地震位错理论建立理论同震变化和大地测量观测值之间的关系式;其次,以2011年Tohoku-Oki地震（M_W9.0）为例,反演体现局部构造特征的地震位错Love数和格林函数.结果表明：反演得到的位错Love数与PREM模型下的位错Love数随深度和阶数变化不同,反映出局部三维地球模型的构造差异,由此计算的同震变化跟实际大地测量观测值的吻合度提高了~60%~~80%.通过大地测量观测数据反演的地震位错Love数能体现局部地球真实的构造信息,为该地区地震研究提供更加精确的地震位错格林函数.